Pca-based portfolio margining

ABSTRACT

A computer implemented method determines a margin requirement for a financial product portfolio. Market conditions for the financial product portfolio are characterized by a zero curve. The method includes producing a plurality of scenario curves, each scenario curve reflecting a principal component analysis (PCA) model of the zero curve with a respective PCA factor of a plurality of PCA factors of the PCA model offset from a corresponding base value for the zero curve, calculating a respective projected value of the financial product portfolio for each scenario curve of the plurality of scenario curves, calculating a loss risk amount for each PCA factor based on the respective projected value and a current value of the financial product portfolio, and determining the margin requirement based on a sum of the loss risk amounts for the plurality of PCA factors.

REFERENCE TO RELATED APPLICATION

This application is a continuation under 37 C.F.R. § 1.53(b) of U.S.patent application Ser. No. 13/956,707, filed Aug. 1, 2013 (AttorneyDocket No. 4672/13001A), the entire disclosure of which is herebyincorporated by reference.

TECHNICAL FIELD

The following disclosure relates to software, systems and methods fordetermining margin requirements in a commodities exchange, derivativesexchange or similar business.

BACKGROUND

A financial instrument trading system, such as a futures exchange,referred to herein also as an “Exchange”, such as the Chicago MercantileExchange Inc. (CME), provides a contract market where financialinstruments, for example futures and options on futures, are traded.Futures is a term used to designate all contracts for the purchase orsale of financial instruments or physical commodities for futuredelivery or cash settlement on a commodity futures exchange. A futurescontract is a legally binding agreement to buy or sell a commodity at aspecified price at a predetermined future time. An option is the right,but not the obligation, to sell or buy the underlying instrument (inthis case, a futures contract) at a specified price within a specifiedtime. The commodity to be delivered in fulfillment of the contract, oralternatively the commodity for which the cash market price shalldetermine the final settlement price of the futures contract, is knownas the contract's underlying reference or “underlier.” The terms andconditions of each futures contract are standardized as to thespecification of the contract's underlying reference commodity, thequality of such commodity, quantity, delivery date, and means ofcontract settlement. Cash Settlement is a method of settling a futurescontract whereby the parties effect final settlement when the contractexpires by paying/receiving the loss/gain related to the contract incash, rather than by effecting physical sale and purchase of theunderlying reference commodity at a price determined by the futurescontract, price.

Options and futures may be based on more abstract market indicators,such as stock indices, interest rates, futures contracts and otherderivatives. An interest rate futures contract, also referred to as aninterest rate future, is a futures contract having an underlyinginstrument/asset that pays interest, for which the parties to thecontract are a buyer and a seller agreeing to the future delivery of theinterest bearing asset, or a contractually specified substitute. Such afutures contract permits a buyer and seller to lock in the price, or inmore general terms the interest rate exposure, of the interest-bearingasset for a future date.

An interest rate swap (“IRS”) is a contractual agreement between twoparties, i.e., the counterparties, where one stream of future interestpayments is exchanged for another, e.g., a stream of fixed interest ratepayments in exchange for a stream of floating interest rate payments,based on a specified principal amount. An IRS contract may be used tolimit or manage exposure to fluctuations in interest rates. One commonform of IRS contract exchanges a stream of floating interest ratepayments on the basis of the 3-month London interbank offered rate for astream of fixed-rate payments on the basis of the swap's fixed interestrate. Another common form of IRS contract, knows as an overnight indexswap, exchanges at its termination a floating rate payment determined bydaily compounding of a sequence of floating interest rates on the basisof an overnight interest rate reference (e.g., the US daily effectivefederal funds rate, or the European Overnight Index Average (EONIA))over the life of the swap, for a fixed rate payment on the basis ofdaily compounding of the overnight index swap's fixed interest rate overthe life of the swap.

An IRS futures contract is one in which the underlying instrument is aninterest rate swap. As such, an IRS futures contract permits “synthetic”exposure to the underlying interest rate swap, i.e., without entailingactual ownership of the underlying IRS contract.

Typically, the Exchange provides for a centralized “clearing house”through which all trades made must be confirmed, matched, and settledeach day until offset or delivered. The clearing house is an adjunct tothe Exchange, and may be an operating division of the Exchange, which isresponsible for settling trading accounts, clearing trades, collectingand maintaining performance bond funds, regulating delivery, andreporting trading data. The essential role of the clearing house is tomitigate credit risk. Clearing is the procedure through which theClearing House becomes buyer to each seller of a futures contract, andseller to each buyer, also referred to as a novation, and assumesresponsibility for protecting buyers and sellers from financial loss dueto breach of contract, by assuring performance on each contract. Aclearing member is a firm qualified to clear trades through the ClearingHouse.

The Clearing House of an Exchange clears, settles and guarantees allmatched transactions in contracts occurring through the facilities ofthe Exchange. In addition, the Clearing House establishes and monitorsfinancial requirements for clearing members and conveys certain clearingprivileges in conjunction with the relevant exchange markets.

The Clearing House establishes clearing level performance bonds(margins) for all products of the Exchange and establishes minimumperformance bond requirements for customers of such products. Aperformance bond, also referred to as a margin requirement, correspondswith the funds that must be deposited by a customer with his or herbroker, by a broker with a clearing member or by a clearing member withthe Clearing House, for the purpose of insuring the broker or ClearingHouse against loss on open futures or options contracts. This is not apart payment on a purchase. The performance bond helps to ensure thefinancial integrity of brokers, clearing members and the Exchange as awhole. The Performance Bond to Clearing House refers to the minimumdollar deposit, which is required by the Clearing House from clearingmembers in accordance with their positions. Maintenance, or maintenancemargin, refers to a sum, usually smaller than the initial performancebond, which must remain on deposit in the customer's account for anyposition at all times. The initial margin is the total amount of marginper contract required by the broker when a futures position is opened. Adrop in funds below this level requires a deposit back to the initialmargin levels, i.e. a performance bond call. If a customer's equity inany futures position drops to or under the maintenance level because ofadverse price action, the broker must issue a performance bond/margincall to restore the customer's equity. A performance bond call, alsoreferred to as a margin call, is a demand for additional funds to bringthe customer's account back up to the initial performance bond levelwhenever adverse price movements cause the account to go below themaintenance.

The margin requirements for IRS contracts are typically set at apercentage of the notional amount of the contract. As a result, marginsfor IRS contracts may be unrealistically high and appear to traders ashaving little to no bearing on the market risk incurred by the exchangein connection with the derivatives.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a block diagram of an exemplary system for trading IRScontracts or other financial products according to the disclosedembodiments.

FIG. 2 is a block diagram of an exemplary system for determining amargin requirement for an IRS contract or other financial product (orproduct portfolio) in accordance with one embodiment.

FIG. 3 is a flow chart diagram of an exemplary method for determining amargin requirement for an IRS contract or other financial product (orproduct portfolio) in accordance with one embodiment.

FIG. 4 shows an illustrative embodiment of a general computer system foruse with the system of FIG. 1 and/or the system of FIG. 2 and/or forimplementing the method of FIG. 3.

FIG. 5 is a graphical plot depicting an exemplary zero month curve forthree-month LIBOR IRS contracts and a corresponding set of shocked orscenario curves in accordance with one embodiment.

FIG. 6 is a graphical plot depicting a simplified example of a PCAfactor-based technique for generating scenario curves in accordance withone embodiment.

FIG. 7 is a graphical plot depicting exemplary weights of a three-factorPCA model in accordance with one embodiment.

FIG. 8 is a graphical plot depicting an exemplary charge function forincorporating a reserve charge into a margin requirement determinationbased on a factor-deficient PCA model in accordance with one embodiment.

FIGS. 9A-9C are graphical plots depicting margin requirements resultingfrom implementing PCA-based margining in accordance with one embodiment.

DETAILED DESCRIPTION

The disclosed embodiments relate to determining margin requirements forportfolios having interest rate swap (IRS) contracts and other financialproducts whose market price or conditions are characterized by a zerocurve. The margining is based on a principal component analysis (PCA)model of the zero curve. The PCA models of the disclosed embodimentssupport margining at an adequate coverage level (e.g., 99%) withouthaving to generate a large set of hypothetical scenarios and toimplement the corresponding portfolio evaluations. The large set ofpossible hypothetical scenarios arises in part from the horizon of thezero curves (e.g., quarterly over 30, 40, or 50 years), which are oftenconstructed on a daily basis based on the prices of a collection ofinstruments to depict where investments would be arbitrage-free. Thedisclosed embodiments use the PCA model to determine a morecomputationally manageable set of hypothetical scenario curves that arenonetheless capable of addressing correlation and volatility riskspresented by the portfolios.

The use of a PCA model of a zero curve supports the generation ofhypothetical scenario zero curves not limited to historicalobservations. The PCA factors are varied, or shocked, to generatehypothetical zero curve scenarios. Applying shocks to the PCA model of adesired magnitude allows the margin determination to be more forwardlooking than other techniques based on historical return data. Theshocks are not limited to historical observations.

A computationally manageable number of scenario curves are produced byindependently shocking or varying a respective one of the PCA factors.For example, the margin requirement determination may use only a pair ofscenario curves for each PCA factor. Scenario curves may be producedonly for variances along the coordinate axes defined by the PCA factors.In a three-factor embodiment, only six scenario curves are generated.Two scenario curves are generated for each factor, one for a positivevariance from a base value, and the other for an equal and oppositevariance.

The limited number of scenario curves is nonetheless sufficient formargining purposes. The limited number stands in contrast to fullPCA-based simulations (e.g., Monte Carlo simulations) in which billionsor trillions (e.g., 2¹⁶) of scenarios are produced, evaluated andprocessed. While such simulations may be feasible on a one-time basisfor a market participant in the midst of an investment decision, thecalculations and other processing tasks involved in margindeterminations may be implemented repeatedly (e.g., on a daily basis foreach trader). The disclosed embodiments provide a mechanism for using aPCA model without testing all of the possible scenarios. The disclosedembodiments may thus decrease the processing load presented by themargin requirement determination. Despite the decreased processing, thedisclosed embodiments are nonetheless able to manage risk for over 99%of the scenarios.

The disclosed embodiments may further improve the processing time byoptimizing the number of PCA factors to be processed. Risk managementsystems may have insufficient processing resources to process all of thefactors (and resulting scenario curves) for a PCA model that achieves99% coverage. As described below, in some embodiments, the PCA model isinstead factor-deficient. The deficiency may be addressed through areserve or add-on charge function configured to address how the PCAmodel is not portfolio-specific. The charge function is used to add areserve charge to the margin requirement. With the reserve charge, atarget coverage of 99% may be achieved with only the top three PCAfactors used to model the zero curve. The PCA model may thus include anoptimized number of factors to achieve or meet a performance bondcoverage target. The optimized number of factors may also lead toimproved computational performance through a reduced number of scenariosto be generated, processed, and evaluated.

As discussed above, an IRS contract is a contractual agreement betweentwo parties, i.e., the counterparties, where one stream of futureinterest payments is exchanged for another, e.g., a stream of fixedinterest rate payments in exchange for a stream of floating interestrate payments, based on a specified principal amount. An IRS contractmay be used to limit or manage exposure to fluctuations in interestrates.

Although described below in connection with examples involving interestrate swap (IRS) contracts based on LIBOR rates, the methods describedherein are well suited for determining margin requirements for a varietyof interest rate swaps, interest rate-based products, or otherderivative financial products, now available or hereafter developed. Forexample, the disclosed embodiments may be useful in connection with anyproduct with an uncertain yield curve, such as EuroDollar futurescontracts, as well as any forward contract using the yield curve fordiscounting, or otherwise characterized by a yield curve. The parametersof the IRS or other interest rate-based contract may vary from theexamples shown. For example, the disclosed methods and systems are notlimited to any particular currency, type (e.g., fixed-for-floating,floating-for-floating, fixed-for-fixed, same or different currencies),duration, rate reset arrangement, payment frequency, or other contractparameter. While the disclosed embodiments are discussed in relation toIRS contracts, the disclosed embodiments may be applicable to otherbilateral contracts, equity, options or futures trading system or marketnow available or later developed.

While the disclosed embodiments may be described in reference to theCME, it will be appreciated that these embodiments are applicable to anyExchange. Such other Exchanges may include a clearing house that, likethe CME Clearing House, clears, settles and guarantees all matchedtransactions in contracts of the Exchange occurring through itsfacilities. In addition, such clearing houses establish and monitorfinancial requirements for clearing members and conveys certain clearingprivileges in conjunction with the relevant exchange markets.

The disclosed embodiments are also not limited to uses by a clearinghouse or Exchange for purposes of enforcing a performance bond or marginrequirement. For example, a market participant may use the disclosedembodiments in a stress test or other simulation of the performance of aportfolio. In such cases, the margin requirement determination may beuseful as an indication of a value at risk rather than a performancebond. The disclosed embodiments may also be used by market participantsor other entities to forecast or predict the effects of a prospectiveposition on the margin requirement of the market participant.

The methods and systems described herein may be integrated or otherwisecombined with other risk management methods and systems, such as therisk management methods and systems described in U.S. Patent PublicationNo. 2006/0265296 (“System and Method for Activity Based Margining”), theentire disclosure of which is incorporated by reference. For example,the methods and systems described herein may be configured as acomponent or module of the risk management systems described in theabove-referenced patent publication. Alternatively or additionally, thedisclosed methods may generate data to be provided to the systemsdescribed in the above-referenced patent publication. For example, themargin requirements determined by the disclosed embodiments may be addedto the margin requirement(s) determined by the other risk managementmethod or system.

In one embodiment, the disclosed methods and systems are integrated orotherwise combined with the risk management system implemented by CMEcalled Standard Portfolio Analysis of Risk™ (SPAN®). The SPAN systembases performance bond requirements on the overall risk of theportfolios using parameters as determined by CME's Board of Directors,and thus represents a significant improvement over other performancebond systems, most notably those that are “strategy-based” or“delta-based.” Further details regarding SPAN are set forth in theabove-referenced patent publication. The incorporation of the disclosedembodiments into a SPAN-based risk management system may include orinvolve a determination that the risk presented by an IRS position (orportfolio of positions) is offset to an extent by the risk presented byone or more non-IRS positions. In such cases, the total marginrequirement may be lower than a simple addition of the constituentmargin requirements.

The embodiments may be described in terms of a distributed computingsystem. The particular examples identify a specific set of componentsuseful in a futures and options exchange. However, many of thecomponents and inventive features are readily adapted to otherelectronic trading environments. The specific examples described hereinmay teach specific protocols and/or interfaces, although it should beunderstood that the principles involved may be extended to, or appliedin, other protocols and interfaces.

It will be appreciated that the plurality of entities utilizing orinvolved with the disclosed embodiments, e.g. the market participants,may be referred to by other nomenclature reflecting the role that theparticular entity is performing with respect to the disclosedembodiments and that a given entity may perform more than one roledepending upon the implementation and the nature of the particulartransaction being undertaken, as well as the entity's contractual and/orlegal relationship with another market participant and/or the Exchange.

With reference now to the drawing figures, an exemplary trading networkenvironment for implementing trading systems and methods is shown inFIG. 1. An exchange computer system 100 receives orders and transmitsmarket data related to orders and trades to users, such as via wide areanetwork 126 and/or local area network 124 and computer devices 114, 116,118, 120 and 122, as described below, coupled with the exchange computersystem 100.

Herein, the phrase “coupled with” is defined to mean directly connectedto or indirectly connected through one or more intermediate components.Such intermediate components may include both hardware and softwarebased components. Further, to clarify the use in the pending claims andto hereby provide notice to the public, the phrases “at least one of<A>, <B>, . . . and <N>” or “at least one of <A>, <B>, . . . <N>, orcombinations thereof” are defined by the Applicant in the broadestsense, superseding any other implied definitions hereinbefore orhereinafter unless expressly asserted by the Applicant to the contrary,to mean one or more elements selected from the group comprising A, B, .. . and N, that is to say, any combination of one or more of theelements A, B, . . . or N including any one element alone or incombination with one or more of the other elements which may alsoinclude, in combination, additional elements not listed.

The exchange computer system 100 may be implemented with one or moremainframe, desktop or other computers, such as the computer 400described below in connection with FIG. 4. A user database 102 may beprovided which includes information identifying traders and other usersof exchange computer system 100, such as account numbers or identifiers,user names and passwords. An account data module 104 may be providedwhich may process account information that may be used during trades.

A match engine module 106 may be included to match bid and offer pricesand may be implemented with software that executes one or morealgorithms for matching bids and offers. The match engine module 106 maybe in communication with one or more of the local area network 124, thewide area network 126, or other elements of the exchange computer system100 to receive data indicative of the orders from the marketparticipants.

A trade database 108 may be included to store information identifyingtrades and descriptions of trades. In particular, a trade database maystore information identifying the time that a trade took place and thecontract price. An order book module 110 may be included to compute orotherwise determine current bid and offer prices. A market data module112 may be included to collect market data and prepare the data fortransmission to users. A risk management module 134 may be included tocompute and determine a user's risk utilization in relation to theuser's defined risk thresholds. The risk management module 134 may alsobe configured to determine risk assessments or exposure levels inconnection with positions held by a market participant.

The risk management module 134 may be configured to administer, manageor maintain one or more margining mechanisms implemented by the exchangecomputer system 100. Such administration, management or maintenance mayinclude managing a number of database records reflective of marginaccounts of the market participants. In some embodiments, the riskmanagement module 134 implements one or more aspects of the disclosedembodiments, including, for instance, PCA-based margining in connectionwith IRS portfolios, as described below.

An order processing module 136 may be included to decompose delta-basedand bulk order types for processing by the order book module 110 and/orthe match engine module 106. The order processing module 136 may also beused to implement one or more procedures related to clearing an order.

In the example of FIG. 1, the exchange computer system 100 also includesa settlement module 140 (or settlement processor or other paymentprocessor) to provide one or more functions related to settling orotherwise administering transactions cleared by the Exchange.Settlement-related functions need not be limited to actions or eventsoccurring at the end of a contract term. For instance, in someembodiments, settlement-related functions may include or involve dailyor other MTM settlements for margining purposes. For example, thesettlement module 140 may be configured to communicate with the tradedatabase 108 (or the memory(ies) on which the trade database 108 isstored) and/or to determine a payment amount based on a spot price, theprice of the futures contract or other financial instrument, or otherprice data, at various times. The determination may be made at one ormore points in time during the term of the financial instrument inconnection with a margining mechanism. For example, the settlementmodule 140 may be used to determine a MTM amount on a daily basis duringthe term of the financial instrument. Such determinations may also bemade on a settlement date for the financial instrument for the purposesof final settlement.

In some embodiments, the settlement module 140 may be integrated to anydesired extent with one or more of the other modules or processors ofthe exchange computer system 100. For example, the settlement module 140and the risk management module 134 may be integrated to any desiredextent. In some cases, one or more margining procedures or other aspectsof the margining mechanism(s) may be implemented by the settlementmodule 140.

The exchange computer system 100 may include one or more additionalmodules or processors, including, for instance, a volume control moduleconfigured to, among other things, control the rate of acceptance ofmass quote messages. It will be appreciated that concurrent processinglimits may be defined by or imposed separately or in combination, as wasdescribed above, on one or more of the trading system components,including the user database 102, the account data module 104, the matchengine module 106, the trade database 108, the order book module 110,the market data module 112, the risk management module 134, the orderprocessing module 136, or other component of the exchange computersystem 100.

The trading network environment shown in FIG. 1 includes exemplarycomputer devices 114, 116, 118, 120 and 122, which depict differentexemplary methods or media by which a computer device may be coupledwith the exchange computer system 100 or by which a user maycommunicate, e.g. send and receive trade or other information therewith.It will be appreciated that the types of computer devices deployed bytraders and the methods and media by which they communicate with theexchange computer system 100 is implementation dependent and may varyand that not all of the depicted computer devices and/or means/media ofcommunication may be used and that other computer devices and/ormeans/media of communications, now available or later developed may beused. Each computer device, which may include a computer 400 describedin more detail below with respect to FIG. 4, may include a centralprocessor that controls the overall operation of the computer and asystem bus that connects the central processor to one or moreconventional components, such as a network card or modem. Each computerdevice may also include a variety of interface units and drives forreading and writing data or files and communicating with other computerdevices and with the exchange computer system 100. Depending on the typeof computer device, a user can interact with the computer with akeyboard, pointing device, microphone, pen device or other input devicenow available or later developed.

An exemplary computer device 114 is shown directly connected to exchangecomputer system 100, such as via a T1 line, a common local area network(LAN) or other wired and/or wireless medium for connecting computerdevices, such as the network 420 shown in FIG. 4 and described belowwith respect thereto. The exemplary computer device 114 is further shownconnected to a radio 132. The user of radio 132, which may include acellular telephone, smart phone, or other wireless proprietary and/ornon-proprietary device, may be a trader or exchange employee. The radiouser may transmit orders or other information to the exemplary computerdevice 114 or a user thereof. The user of the exemplary computer device114, or the exemplary computer device 114 alone and/or autonomously, maythen transmit the trade or other information to the exchange computersystem 100.

Exemplary computer devices 116 and 118 are coupled with a local areanetwork (“LAN”) 124 which may be configured in one or more of thewell-known LAN topologies, e.g. star, daisy chain, etc., and may use avariety of different protocols, such as Ethernet, TCP/IP, etc. Theexemplary computer devices 116 and 118 may communicate with each otherand with other computer and other devices which are coupled with the LAN124. Computer and other devices may be coupled with the LAN 124 viatwisted pair wires, coaxial cable, fiber optics or other wired orwireless media. As shown in FIG. 1, an exemplary wireless personaldigital assistant device (“PDA”) 122, such as a mobile telephone, tabletbased compute device, or other wireless device, may communicate with theLAN 124 and/or the Internet 126 via radio waves, such as via WiFi,Bluetooth and/or a cellular telephone based data communicationsprotocol. PDA 122 may also communicate with exchange computer system 100via a conventional wireless hub 128.

FIG. 1 also shows the LAN 124 coupled with a wide area network (“WAN”)126 which may be comprised of one or more public or private wired orwireless networks. In one embodiment, the WAN 126 includes the Internet126. The LAN 124 may include a router to connect LAN 124 to the Internet126. Exemplary computer device 120 is shown coupled directly to theInternet 126, such as via a modem, DSL line, satellite dish or any otherdevice for connecting a computer device to the Internet 126 via aservice provider therefore as is known. LAN 124 and/or WAN 126 may bethe same as the network 420 shown in FIG. 4 and described below withrespect thereto.

The operations of computer devices and systems shown in FIG. 1 may becontrolled by computer-executable instructions stored on anon-transitory computer-readable medium. For example, the exemplarycomputer device 116 may include computer-executable instructions forreceiving order information from a user and transmitting that orderinformation to exchange computer system 100. In another example, theexemplary computer device 118 may include computer-executableinstructions for receiving market data from exchange computer system 100and displaying that information to a user.

Numerous additional servers, computers, handheld devices, personaldigital assistants, telephones and other devices may also be connectedto the exchange computer system 100. Moreover, the topology shown inFIG. 1 is merely an example and that the components shown in FIG. 1 mayinclude other components not shown and be connected by numerousalternative topologies.

As shown in FIG. 1, the risk management module 134 of the exchangecomputer system 100 may implement one or more aspects of the PCA-basedmargining techniques of the disclosed methods and systems, as will bedescribed with reference to FIG. 2. It will be appreciated the disclosedembodiments may be implemented as a different or separate module of theexchange computer system 100, or a separate computer system coupled withthe exchange computer system 100 so as to have access to margin accountrecord, pricing, and/or other data. As described above, the disclosedembodiments may be implemented as a centrally accessible system or as adistributed system, e.g., where some of the disclosed functions areperformed by the computer systems of the market participants.

As an intermediary, the Exchange 108 bears a certain amount of risk ineach transaction that takes place. To that end, risk managementmechanisms protect the Exchange 108 via the Clearing House. The ClearingHouse establishes clearing level performance bonds (margins) for all CMEproducts and establishes minimum performance bond requirements forcustomers of CME products. A performance bond, also referred to as amargin, corresponds with the funds that must be deposited by a customerwith his or her broker, by a broker with a clearing member or by aclearing member with the Clearing House, for the purpose of insuring thebroker or Clearing House against loss on open futures or optionscontracts. This is not a part payment on a purchase. The performancebond helps to ensure the financial integrity of brokers, clearingmembers and the Exchange as a whole. The Performance Bond to ClearingHouse refers to the minimum dollar deposit required by the ClearingHouse from clearing members in accordance with their positions.Maintenance, or maintenance margin, refers to a sum, usually smallerthan the initial performance bond, which must remain on deposit in thecustomer's account for any position at all times. The initial margin isthe total amount of margin per contract required by the broker when afutures position is opened. A drop in funds below this level requires adeposit back to the initial margin levels, i.e. a performance bond call.If a customer's equity in any futures position drops to or under themaintenance level because of adverse price action, the broker must issuea performance bond/margin call to restore the customer's equity. Aperformance bond call, also referred to as a margin call, is a demandfor additional funds to bring the customer's account back up to theinitial performance bond level whenever adverse price movements causethe account to go below the maintenance.

As described below in connection with the exemplary embodiments of FIGS.2 and 3, one or more of the modules of the Exchange computer system 100may be configured to determine a margin requirement for a financialproduct portfolio involving one or more positions having a marketcharacterized by a zero curve. In some cases, the financial productportfolio includes a number of IRS positions. A PCA-based model of thezero curve is generated based on historical return data, to whichweighting factors (e.g., exponentially weighted moving average (EWMA)weighting factors) may be applied to adjust the historical return datato make near-term returns more important older returns. Such weightingmay reduce portfolio over-coverage while maintaining a desired targetcoverage criterion (e.g., 99%). The PCA-based model, in turn, supportsthe deterministic production of a number of scenario curves that maythen be used to determine projected gains and losses for the portfolio.

Principal component analysis is an orthogonal transformation of anoriginal set of variables, which may be correlated to some extent, intolinearly uncorrelated variables. In this case, the original variablesare the daily (or other periodic) returns for each of the tenors of thefinancial products that may be present in the portfolio. The return datamay be arranged in or represented by the zero curve, also referred to asthe base curve. The tenors may be representative of the maturity datefor the financial product. Because the number of tenors may be quitelarge, principal component analysis is useful for reducing thedimensionality of the correlation matrix (e.g., 120*120 quarters for IRScontracts). The principal component analysis may reduce thedimensionality to only a few (e.g., three) factors through eigenvaluedecomposition, singular value decomposition, or other decomposition.

The PCA model transforms the original matrix of historical zero curvereturns X(i,j) into an orthogonal space of principal components orfactors P, such that P=X*W and P′*P=V, where

-   -   V is the eigenvalue matrix of P and is indicative of the factor        variation;    -   W is the eigenvector orthogonal matrix of factor sensitivities;    -   i is the index for the day during the period of returns (e.g.,        in a five year period, the index i runs from 1 to 1260); and    -   j is the index for the tenor (or maturity) of the zero curve        (e.g., the index j may run from 1 to 1120 for forty years worth        of quarters). The eigenvectors and eigenvalues may represent the        sensitivities and volatilities used to produce the hypothetical        scenarios.

In some embodiments, the first three significant factors of the PCAmodel are used to produce the scenario curves. The first threesignificant factors are representative of trend (or level), tilt (orslope), and shape (or curvature). Additional factors may be used. Thevolatility of each factor in the model may then be independently orseparately varied, shocked, or otherwise offset to produce thehypothetical scenario curves. For each scenario curve, one of thefactors may be varied or offset in the eigenvalue matrix V to a desiredextent. For example, the factor may be varied or offset by an amountthat falls within a range from about two to about four standarddeviations of the variation (or distribution) for that factor. Eachfactor itself has a variance, the square root of which is the standarddeviation. As described below, the independent or separate variation ofthe factors of the PCA model helps to keep the number of scenario curvesat a manageable level.

The hypothetical scenario curves are produced from the orthogonalfactors of the PCA model as follows:

-   -   Scenario Curve=Base Curve*exp(W*sqrt(V)*Factor Weight),        where the base curve is the current zero curve, and the factor        weights are factor-specific parameters, which may be calibrated        or otherwise predetermined through, e.g., back testing of the        PCA model. FIG. 7 shows exemplary factor weights for a        three-factor model. For each scenario curve, the variance V may        be set to a level to reach a desired offset for the        corresponding PCA factor. The desired offset may fall in a range        from about two standard deviations to about four standard        deviations of a mean value for the PCA factor. For example, the        shocks or desired offsets may range over nine levels, namely −4,        −3, −2, −1, 0, 1, 2, 3, and 4, of the standard deviation. In one        embodiment, equal and opposite offsets are used to generate a        pair of curves for each PCA factor. The offsets may be uniform        across the factors.

Once the hypothetical scenario curves are produced, loss risk data for agiven portfolio may be calculated. The current value of the portfolio iscalculated based on the current or base zero curve. A hypothetical valueof the portfolio is calculated based on a respective one of the scenariocurves. Loss risk data for each scenario curve may then be calculated bycalculating the difference between the current and hypothetical values.Scenario curves resulting in a gain for the portfolio may bedisregarded. The loss risk data may be factor-specific, e.g., specificto the offset PCA factor.

A margin for each PCA factor may be calculated by taking the absolutevalue of the loss risk data for each factor. The factor-specific marginsmay thus be representative of a portion of the maximum hypothetical lossof each portfolio. The factor-specific margins may not be symmetric fromthe points of view of the buyer and seller. The margin requirement forthe portfolio is then determined as the sum of the factor-specificmargins.

The scenario curves produced via the disclosed embodiments may reduceover-coverage without falling below a desired level of coverage (e.g.,99%), as well as account for volatility changes automatically (e.g.,without forcing a user to additionally forecast a volatility regimechange). These benefits may be provided despite a reduction in thenumber of PCA factors relied upon in the margin determination process asdescribed below.

In some cases, the number of factors in the PCA model may be sufficientto cover a desired fraction (e.g., 99%) of the variation presented bythe historical zero curve returns, but insufficient to handle theadditional variability presented by a specific portfolio at the samelevel of protection (e.g., 99%). For example, a three-factor PCA modelmay not adequately cover the variation introduced via portfoliosensitivities (e.g., to a particular tenor). For instance, a portfoliomay have multiple positions within a particular tenor. The value at riskincreasingly becomes dependent on the portfolio sensitivity, or PV01. Toaddress such sensitivities, additional factors may be incorporated intothe PCA model. In an example attempting to achieve 99% coverage, the PCAmodel may include nine factors. However, with all nine factors, thenumber of scenarios could be large enough to be prohibitive incomputation time and/or cost.

The number of scenarios may be limited to more reasonable computationtimes and costs by optimizing (e.g., reducing) the number of factorswithin the PCA model from the level associated with 99% portfoliocoverage. Therefore, in some embodiments, the number of factors in thePCA model is reduced from the level required for 99% portfolio coverage.The PCA model may thus be referred to as factor-deficient.

The contribution from each factor for a portfolio may be calculated as aratio of Portfolio Factor variance over Total Portfolio Factor variance.Portfolio Factor variance may be calculated as a function of thePosition PV01 in each maturity j, the factor sensitivity, and the factorvolatility. The number of significant factors (N_(s)) may then becalculated as the minimum number of factors needed to meet theperformance bond coverage target of 99%, as set forth below:

-   -   N_(s)=min n−>Sum C_(j)>=0.99        -   j=1, n    -   where Portfolio Factor (j) Contribution to total variance is        -   C_(j)=W_(j)/Sum W_(j)            -   i=1, N    -   and Portfolio Factor (i) variation is        -   W_(j)=Sum(PV01(i)*F_(ij))²*V_(j)            -   i=1, M            -   where F_(ij) is the matrix of factor (j) sensitivities                (eigenvector) to the zero curve in maturity i, V_(j) is                the factor j variation, and PV01(i) is the position                duration in maturity i=1,M.

While back testing of the PCA model demonstrated that nine factors aresufficient number to satisfy the 99% target, the number of factors usedin the PCA model may be further reduced to the first three significantfactors, i.e., level, slope, and curvature significant factors, whichcover 99% variation in zero curve historical shocks. To compensate forsuch factor reduction and possible margin under-coverage due toportfolio sensitivities arising from the deficiency of the PCA model, incertain circumstances, the margin requirement is adjusted through theaddition of a reserve charge. The circumstances or conditions underwhich the reserve charge is added may address when the nature of theportfolio may be likely to increase risk. The reserve charge may beempirically based as described below.

FIG. 2 depicts a block diagram of a system 200 operative to determine amargin requirement for a financial product portfolio. Market conditionsfor the financial product portfolio are characterized by a zero curve.The financial product portfolio may be part of a broader portfoliohaving any number of positions involving other types of financialproducts (e.g., products for which market conditions are notcharacterized by a zero curve). In some embodiments, the system 200 maycorrespond with, or implement, the risk management module 134 and/orother module of the exchange computer system 100. The system 200 maythus be implemented as part of the exchange computer system 100described above.

One or more of the above-described modules of the Exchange computersystem 100 may be used to gather or obtain data to support the marginrequirement determination by the system 200. For example, the marketdata module 112 may be used to receive, access, or otherwise obtainhistorical return data. The trade database 108 may be used to receive,access, or otherwise obtain data indicative of the current positionswithin the portfolio of a market participant.

The system 200 includes a processor 202 and a memory 204 coupledtherewith which may be implemented as a processor 402 and memory 404 asdescribed below with respect to FIG. 4. The system 200 further includesfirst logic 206 stored in the memory 204 and executable by the processor202 to cause the processor 202 to generate a PCA model of the zerocurve. The PCA model includes a set of PCA factors. The set may includeonly the three most significant factors (level, slope, and curvature),even if not including any further factors into the model may result ininsufficient coverage for all portfolios absent the incorporation of areserve charge as described herein. The PCA model may thus be afactor-deficient model of portfolios characterized by the zero curve.Additional factors may be incorporated into the model in otherembodiments, regardless of whether the reserve charge is used to adjustthe margin requirement.

The first logic 206 may configure the processor 402 to apply weights todecay the historical return data (e.g., log return data). To generate amatrix of decayed returns, the log return data may be scaled byweighting factors. The weighting factors may vary such that more recentreturn data is weighted more heavily than less recent return data. ThePCA model may accordingly be most reactive to, or reflective of, themost recent volatility or returns. In one embodiment, an exponentiallyweighted moving average (EWMA) decay is applied to the historical returndata. Weights of the EWMA decay that decrease exponentially as the datagets older are applied to the historical return data. Other movingaverage, time series, or decay techniques may be used.

The first logic 206 may then process the decayed return matrix togenerate the PCA model. The PCA factors, eigenvectors, and eigenvaluesof a covariance matrix for the zero curve may be generated.

One example of the application of an EWMA decay of an original logreturns matrix X to produce decayed matrix X is as follows.

-   -   X(i,j)=X(i,j)*exp(−i/tau)*w(i)        where—    -   i represents a look back observation from a 5 year historical        period T (i=1,1260);    -   tau represents a decay rate (which may be set in back testing        to, e.g., 252, which is equivalent to a risk metrics EWMA lambda        of 96.1%); and    -   w(i) equals the sqrt (T/SUM exp(−i/tau)² are weights chosen to        satisfy the following normalization condition:    -   SUM(exp(−i/tau)*w(i))²/T=1

The system 200 further includes second logic 208 stored in the memory204 and executable by the processor 202 to cause the processor 202 toproduce a plurality of scenario curves. Each scenario curve reflects thePCA model of the zero curve with a respective one of the plurality ofPCA factors offset from a corresponding base value for the zero curve.The other PCA factors may not be offset from their corresponding basevalues. Alternatively, one or more of the other PCA factors are offsetfrom their base values.

In one embodiment, a pair of scenario curves is produced for each PCAfactor. For example, one of the scenario curves may be produced for apositive offset from the base value, while the other scenario curve maybe produced for an equal and opposite (or negative) offset from the basevalue. Fewer or additional scenario curves may be produced.

The magnitude of the offsets reflects the severity of the shock appliedto the PCA model of the zero curve. The magnitude of the offsets mayvary across the PCA factors. In some embodiments, the offset for eachPCA factor falls in a range from about two to about four standarddeviations of the distribution of the PCA factor.

The offset magnitude(s) may be selected or predetermined by a user ofthe system 200. For example, the second logic 208 may be executable tocause the processor 202 to generate a user interface to obtain theoffset magnitude(s). Alternatively or additionally, the system 200obtains the offset magnitude(s) automatically in connection with backtesting of the PCA model. In this embodiment, data indicative of theoffsets is stored in the memory 204 in a data structure 209.

The system 200 further includes third logic 210 stored in the memory 204and executable by the processor 202 to cause the processor 202 tocalculate a respective projected value of the financial productportfolio for each scenario curve. Once the scenario curves areproduced, each scenario curve may be used to calculate a respectiveprojected or hypothetical value of the financial product portfolio.

The system 200 further includes fourth logic 212 stored in the memory204 and executable by the processor 202 to cause the processor 202 tocalculate a loss risk amount for each PCA factor. The loss risk amountis calculated based on the respective projected and current values ofthe financial product portfolio. For example, the projected value may besubtracted from the current value to calculate the loss risk amount.

In embodiments having a pair of scenario curves for each PCA factor, thefourth logic 212 may be further executable by the processor 202 todetermine gain and loss amounts for each PCA factor based on the pair ofscenario curves. One of the scenario curves results in a gain, while theother results in a loss. Taking the absolute value of the loss may beused to calculate the loss risk amount for each PCA factor. Each lossrisk amount is specific to a particular PCA factor and may thus beconsidered to be representative of a factor-specific margin.

The system 200 further includes fifth logic 214 stored in the memory 204and executable by the processor 202 to cause the processor 202 todetermine the margin requirement based on a sum of the loss risk amountsfor the plurality of PCA factors. The factor-specific margins are summedto arrive at the margin requirement.

In the embodiment of FIG. 2, the system 200 further includes sixth logic216 stored in the memory 204 and executable by the processor 202 tocause the processor 202 to adjust the margin requirement in certaincircumstances. The sixth logic 216 causes the processor 202 to calculatea reserve charge for each tenor in the financial product portfolio whena reserve condition is satisfied. The processor 202 then adds thereserve charge to the sum of the loss risk amounts to adjust (increase)the margin requirement. The sixth logic 216 may specify one or morereserve conditions. In one example, the reserve condition is met if theportfolio is such that a ratio of a net notional amount to a grossnotional amount is less than or equal to a first threshold, or if theportfolio has a gross weighted average maturity (WAM) is greater than asecond threshold, or if a net WAM of the portfolio is less than or equalto a third threshold. Fewer, alternative, or additional reserveconditions may be used.

In the event one or more of the reserve conditions is met, then thesixth logic 216 may be configured to cause the processor 202 to scale acharge parameter by a price sensitivity of the tenor and an empiricalscale factor. The contribution of each of the high order (or lesssignificant) factors (e.g., higher than the third factor) to totalvariation in a particular zero curve tenor (i) may be expressed as acharge parameter per basis point as follows:

-   -   Charge(i)=√Sum V_(j)*F_(ij) ²        -   j=4, N            The portfolio reserve charge may thus be based on the factor            sensitivity matrix of the PCA model and the offsets in the            PCA factors used to determine the set of scenario curves.

The portfolio reserve charge may have two components. The firstcomponent is time-dependent, while the second component isportfolio-dependent. In some embodiments, the portfolio reserve chargein tenor (i) may be expressed using above the charge for tenor (i), theprice sensitivity or PV01 duration in tenor (i), and a reserve scaleparameter to target 99% coverage as follows:

Reserve Charge(i)=Charge(i)*PV01(i)*Scale

Based on the results of back testing of the PCA model, it was found thatthe charge may be approximated as an exponential function of time tomaturity. An exemplary function is shown in FIG. 8.

The portfolio reserve charge may be applied on a trade-by-trade orposition-by-position basis when one or more conditions are met. Theportfolio reserve charge may be applied on a trade level to haveportfolio netting benefits. For instance, a spread portfolio with twopositions, one long in tenor x and one short in tenor y, would have anetting benefit because the PV01 in tenors x and y have different signs.

In one embodiment, the portfolio reserve charge is applied in thefollowing conditions:

-   -   the absolute value of the ratio of Net Notional to Gross        Notional is less than or equal to 0.4;    -   the gross weighted average maturity (WAM) is greater than or        equal to 15; and    -   the absolute value of the net WAM is less than or equal to 1.        The reserve charge for a particular tenor may then be added to        the margin requirement for a portfolio that falls in any of the        above categories.

The above-described logic may be arranged in any number of modules orother logic units. For example, the sixth logic 216 may be integratedwith the fifth logic 214 to any desired extent. The fourth logic 212 andthe fifth logic 214 may be integrated to any desired extent. Fewer,alternative, or additional logic units may be included.

Referring to FIG. 3, a computer implemented method is configured inaccordance with one embodiment to determine a margin requirement for afinancial product portfolio. Market conditions for the financial productportfolio are characterized by a zero curve, or base zero curve, asdescribed above. The computer-implemented method may be implemented toany desired extent by the system 200 of FIG. 2, the system described inconnection with FIG. 4, the processor 202 (FIG. 2), and/or any otherprocessor. In some cases, the method is implemented by an exchange.Alternatively, the method is implemented by a market participant orother entity for which the margin requirement may be representative of avalue at risk (or potential value at risk).

The computer implemented method may begin with the generation (block300) of a PCA model for the zero curve. The PCA model may be generatedfrom historical return data, which may be selected, received, orotherwise obtained (block 302). The PCA model may be based on log returndata. In the embodiment of FIG. 3, a decayed log return matrix iscalculated (block 304) via an EWMA procedure. A number of PCA factorsmay then be determined (block 306) based on the decayed log returnmatrix.

The PCA model may include the three most significant PCA factors, namelylevel, slope, and curvature. Thus, in some cases, the PCA model does notinclude PCA factors beyond level, slope, and curvature. The PCA modelmay thus be configured as a factor-deficient model, as described above.

In some cases, the PCA model and factor data thereof may already begenerated. Once the PCA model is available, the PCA model may be usedany number of times as representative of a base curve from whichscenario curves are later produced. For example, the PCA model may begenerated daily. Alternatively, the PCA model may be generated (and thusupdated) once per week or at some other interval. The scenario curvesand subsequent margin requirements may use the PCA model as the basecurve throughout the week or other base curve interval. In someembodiments, the PCA model may be used for margining the portfolios ofmultiple market participants.

A plurality of scenario curves are produced (block 308). Each scenariocurve is based on the PCA model of the zero curve (or base curve). Eachscenario curve then reflects an offset in a respective one of the PCAfactors. The respective factor is offset from a corresponding base valuefor the zero curve, while the other PCA factors are not offset for thescenario curve. Each scenario curve may thus be indicative of afactor-specific shocking of the zero curve. The offset(s) may beobtained (block 310) in a variety of ways, including a dedicated userinterface and/or via access to a data structure. The offset for each PCAfactor may fall in a range from about two to about four standarddeviations of a distribution of the PCA factor, as described above.

A pair of scenario curves may be produced for variation in each PCAfactor. Each PCA factor may thus be varied by an equal and oppositeoffset. One scenario curve may have a positive offset, while anotherscenario curve may have a negative offset.

A respective projected value of the financial product portfolio iscalculated (block 312) for each scenario curve of the plurality ofscenario curves, as described above. A loss risk amount for each PCAfactor may then be calculated (block 314) based on the respectiveprojected value and a current value of the financial product portfolio.Each loss risk amount may be calculated by determining (block 316) gainand loss amounts for each PCA factor based on the pair of scenariocurves, and by taking (block 318) the absolute value of the loss amount.A margin requirement for the portfolio is determined (block 320) basedon a sum of the loss risk amounts for the plurality of PCA factors.

The margin requirement determination may include an adjustment based ona reserve charge calculation. In the embodiment of FIG. 3, a decisionblock 322 determines whether one or more reserve conditions is present,satisfied, or applicable to the portfolio (or a position therein). Ifyes, then control passes to a block 324 in which a reserve charge iscalculated for each tenor in the portfolio for which the reservecondition is satisfied. The reserve charge(s) are then added (block 326)to the sum of the loss risk amounts to adjust the margin requirement. Ifnone of the reserve conditions is met, then control passes to a block328 in which the margin requirement is enforced or otherwise applied tothe portfolio.

The reserve conditions may vary. As described above, some reserveconditions may be based on whether a ratio of a net notional to a grossnotional is less than or equal to a first threshold, whether a gross WAMis greater than a second threshold, or whether a net WAM is less than orequal to a third threshold.

Calculating the reserve charge for each tenor may include scaling acharge parameter by a price sensitivity of the tenor and an empiricalscale factor. The charge parameter may be based on a factor sensitivitymatrix of the PCA model and offsets in the PCA factors used to determinethe plurality of scenario curves, as described above.

The application of the margin requirement may include crediting ordebiting an account of a market participant, generating an alert orother message regarding a margin call or other margin requirementupdate, and/or incorporating the margin requirement into another marginrequirement for a broader portfolio. For example, the margin requirementdetermined in accordance with the disclosed embodiments may relate tothe IRS contracts within a portfolio that also includes other, non-IRSderivative positions. The margin requirements for such other derivativepositions may be determined via other procedures, such as thosedescribed in the above-referenced patent publication.

Referring to FIG. 4, an illustrative embodiment of a general computersystem 400 is shown. The computer system 400 can include a set ofinstructions that can be executed to cause the computer system 400 toperform any one or more of the methods or computer based functionsdisclosed herein. The computer system 400 may operate as a standalonedevice or may be connected, e.g., using a network, to other computersystems or peripheral devices. Any of the components discussed above maybe a computer system 400 or a component in the computer system 400. Thecomputer system 400 may implement a match engine on behalf of anexchange, such as the Chicago Mercantile Exchange, of which thedisclosed embodiments are a component thereof.

In a networked deployment, the computer system 400 may operate in thecapacity of a server or as a client user computer in a client-serveruser network environment, or as a peer computer system in a peer-to-peer(or distributed) network environment. The computer system 400 can alsobe implemented as or incorporated into various devices, such as apersonal computer (PC), a tablet PC, a set-top box (STB), a personaldigital assistant (PDA), a mobile device, a palmtop computer, a laptopcomputer, a desktop computer, a communications device, a wirelesstelephone, a land-line telephone, a control system, a camera, a scanner,a facsimile machine, a printer, a pager, a personal trusted device, aweb appliance, a network router, switch or bridge, or any other machinecapable of executing a set of instructions (sequential or otherwise)that specify actions to be taken by that machine. In a particularembodiment, the computer system 400 can be implemented using electronicdevices that provide voice, video or data communication. Further, whilea single computer system 400 is illustrated, the term “system” shallalso be taken to include any collection of systems or sub-systems thatindividually or jointly execute a set, or multiple sets, of instructionsto perform one or more computer functions.

As illustrated in FIG. 4, the computer system 400 may include aprocessor 402, e.g., a central processing unit (CPU), a graphicsprocessing unit (GPU), or both. The processor 402 may be a component ina variety of systems. For example, the processor 402 may be part of astandard personal computer or a workstation. The processor 402 may beone or more general processors, digital signal processors, applicationspecific integrated circuits, field programmable gate arrays, servers,networks, digital circuits, analog circuits, combinations thereof, orother now known or later developed devices for analyzing and processingdata. The processor 402 may implement a software program, such as codegenerated manually (i.e., programmed).

The computer system 400 may include a memory 404 that can communicatewith a drive unit 406 and other components of the system 400 via a bus408. The memory 404 may be a main memory, a static memory, or a dynamicmemory. The memory 404 may include, but is not limited to computerreadable storage media such as various types of volatile andnon-volatile storage media, including but not limited to random accessmemory, read-only memory, programmable read-only memory, electricallyprogrammable read-only memory, electrically erasable read-only memory,flash memory, magnetic tape or disk, optical media and the like. In oneembodiment, the memory 404 includes a cache or random access memory forthe processor 402. In alternative embodiments, the memory 404 isseparate from the processor 402, such as a cache memory of a processor,the system memory, or other memory. The memory 404 may be an externalstorage device or database for storing data. Examples include a harddrive, compact disc (“CD”), digital video disc (“DVD”), memory card,memory stick, floppy disc, universal serial bus (“USB”) memory device,or any other device operative to store data.

The memory 404 is operable to store instructions 410 executable by theprocessor 402. The functions, acts or tasks illustrated in the figuresor described herein may be performed by the programmed processor 402executing the instructions 410 stored in the memory 404. Theinstructions 410 may be loaded or accessed from a computer-readablestorage medium 412 in the drive unit 406 or other data storage device.The functions, acts or tasks are independent of the particular type ofinstructions set, storage media, processor or processing strategy andmay be performed by software, hardware, integrated circuits, firm-ware,micro-code and the like, operating alone or in combination. Likewise,processing strategies may include multiprocessing, multitasking,parallel processing and the like.

As shown, the computer system 400 may further include a display unit414, such as a liquid crystal display (LCD), an organic light emittingdiode (OLED), a flat panel display, a solid state display, a cathode raytube (CRT), a projector, a printer or other now known or later developeddisplay device for outputting determined information. The display 414may act as an interface for the user to see the functioning of theprocessor 402, or specifically as an interface with the software storedin the memory 404 or in the drive unit 406.

Additionally, the computer system 400 may include an input device 416configured to allow a user to interact with any of the components ofsystem 400. The input device 416 may be a number pad, a keyboard, or acursor control device, such as a mouse, or a joystick, touch screendisplay, remote control or any other device operative to interact withthe system 400.

In a particular embodiment, as depicted in FIG. 4, the computer system400 may also include an optical or other disk drive unit as the driveunit 406. The disk drive unit 406 may include the computer-readablestorage medium 412 in which one or more sets of instructions 410, e.g.software, can be embedded. Further, the instructions 410 may embody oneor more of the methods or logic as described herein. In a particularembodiment, the instructions 410 may reside completely, or at leastpartially, within the memory 404 and/or within the processor 402 duringexecution by the computer system 400. The memory 404 and the processor402 also may include computer-readable storage media as discussed above.

The present disclosure contemplates a computer-readable medium thatincludes instructions 410 or receives and executes instructions 410responsive to a propagated signal, which may be received via acommunication interface 418. The system 400 may be connected to anetwork 420 to communicate voice, video, audio, images or any other dataover the network 420. Further, the instructions 412 may be transmittedor received over the network 420 via a communication interface 418. Thecommunication interface 418 may be a part of the processor 402 or may bea separate component. The communication interface 418 may be created insoftware or may be a physical connection in hardware. The communicationinterface 418 is configured to connect with a network 420, externalmedia, the display 414, or any other components in system 400, orcombinations thereof. The connection with the network 420 may be aphysical connection, such as a wired Ethernet connection or may beestablished wirelessly as discussed below. Likewise, the additionalconnections with other components of the system 400 may be physicalconnections or may be established wirelessly.

The network 420 may include wired networks, wireless networks, orcombinations thereof. The wireless network may be a cellular telephonenetwork, an 802.11, 802.16, 802.20, or WiMax network. Further, thenetwork 420 may be a public network, such as the Internet, a privatenetwork, such as an intranet, or combinations thereof, and may utilize avariety of networking protocols now available or later developedincluding, but not limited to TCP/IP based networking protocols.

Embodiments of the subject matter and the functional operationsdescribed in this specification can be implemented in digital electroniccircuitry, or in computer software, firmware, or hardware, including thestructures disclosed in this specification and their structuralequivalents, or in combinations of one or more of them. Embodiments ofthe subject matter described in this specification can be implemented asone or more computer program products, i.e., one or more modules ofcomputer program instructions encoded on a computer readable medium forexecution by, or to control the operation of, data processing apparatus.While the computer-readable medium is shown to be a single medium, theterms “computer-readable medium” and “computer-readable storage medium”include a single medium or multiple media, such as a centralized ordistributed database, and/or associated caches and servers that storeone or more sets of instructions. The term “computer-readable medium”shall also include any medium that is capable of storing, encoding orcarrying a set of instructions for execution by a processor or thatcause a computer system to perform any one or more of the methods oroperations disclosed herein. The computer-readable storage medium may beor include a machine-readable storage device, a machine-readable storagesubstrate, a memory device, or a combination of one or more of them. Theterm “data processing apparatus” encompasses all apparatus, devices, andmachines for processing data, including by way of example a programmableprocessor, a computer, or multiple processors or computers. Theapparatus can include, in addition to hardware, code that creates anexecution environment for the computer program in question, e.g., codethat constitutes processor firmware, a protocol stack, a databasemanagement system, an operating system, or a combination of one or moreof them.

In a particular non-limiting, exemplary embodiment, thecomputer-readable medium can include a solid-state memory such as amemory card or other package that houses one or more non-volatileread-only memories. Further, the computer-readable medium can be arandom access memory or other volatile re-writable memory. Additionally,the computer-readable medium can include a magneto-optical or opticalmedium, such as a disk or tapes or other storage device to capturecarrier wave signals such as a signal communicated over a transmissionmedium. A digital file attachment to an e-mail or other self-containedinformation archive or set of archives may be considered a distributionmedium that is a tangible storage medium. Accordingly, the disclosure isconsidered to include any one or more of a computer-readable medium or adistribution medium and other equivalents and successor media, in whichdata or instructions may be stored.

In an alternative embodiment, dedicated hardware implementations, suchas application specific integrated circuits, programmable logic arraysand other hardware devices, can be constructed to implement one or moreof the methods described herein. Applications that may include theapparatus and systems of various embodiments can broadly include avariety of electronic and computer systems. One or more embodimentsdescribed herein may implement functions using two or more specificinterconnected hardware modules or devices with related control and datasignals that can be communicated between and through the modules, or asportions of an application-specific integrated circuit. Accordingly, thepresent system encompasses software, firmware, and hardwareimplementations.

In accordance with various embodiments of the present disclosure, themethods described herein may be implemented by software programsexecutable by a computer system. Further, in an exemplary, non-limitedembodiment, implementations can include distributed processing,component/object distributed processing, and parallel processing.Alternatively, virtual computer system processing can be constructed toimplement one or more of the methods or functionality as describedherein.

Although the present specification describes components and functionsthat may be implemented in particular embodiments with reference toparticular standards and protocols, the invention is not limited to suchstandards and protocols. For example, standards for Internet and otherpacket switched network transmission (e.g., TCP/IP, UDP/IP, HTML, HTTP,HTTPS) represent examples of the state of the art. Such standards areperiodically superseded by faster or more efficient equivalents havingessentially the same functions. Accordingly, replacement standards andprotocols having the same or similar functions as those disclosed hereinare considered equivalents thereof.

The disclosed computer programs (also known as a program, software,software application, script, or code) can be written in any form ofprogramming language, including compiled or interpreted languages. Thedisclosed computer programs can be deployed in any form, including as astandalone program or as a module, component, subroutine, or other unitsuitable for use in a computing environment. Such computer programs donot necessarily correspond to a file in a file system. Such programs canbe stored in a portion of a file that holds other programs or data(e.g., one or more scripts stored in a markup language document), in asingle file dedicated to the program in question, or in multiplecoordinated files (e.g., files that store one or more modules, subprograms, or portions of code). Such computer programs can be deployedto be executed on one computer or on multiple computers that are locatedat one site or distributed across multiple sites and interconnected by acommunication network.

The processes and logic flows described in this specification can beperformed by one or more programmable processors executing one or morecomputer programs to perform functions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, e.g., an FPGA (field programmable gate array) or an ASIC(application specific integrated circuit).

Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andanyone or more processors of any kind of digital computer. Generally, aprocessor may receive instructions and data from a read only memory or arandom access memory or both. The essential elements of a computer are aprocessor for performing instructions and one or more memory devices forstoring instructions and data. Generally, a computer may also include,or be operatively coupled to receive data from or transfer data to, orboth, one or more mass storage devices for storing data, e.g., magnetic,magneto optical disks, or optical disks. However, a computer need nothave such devices. Moreover, a computer can be embedded in anotherdevice, e.g., a mobile telephone, a personal digital assistant (PDA), amobile audio player, a Global Positioning System (GPS) receiver, to namejust a few. Computer readable media suitable for storing computerprogram instructions and data include all forms of non volatile memory,media and memory devices, including by way of example semiconductormemory devices, e.g., EPROM, EEPROM, and flash memory devices; magneticdisks, e.g., internal hard disks or removable disks; magneto opticaldisks; and CD ROM and DVD-ROM disks. The processor and the memory can besupplemented by, or incorporated in, special purpose logic circuitry.

To provide for interaction with a user, embodiments of the subjectmatter described in this specification can be implemented on a devicehaving a display, e.g., a CRT (cathode ray tube) or LCD (liquid crystaldisplay) monitor, for displaying information to the user and a keyboardand a pointing device, e.g., a mouse or a trackball, by which the usercan provide input to the computer. Other kinds of devices can be used toprovide for interaction with a user as well; for example, feedbackprovided to the user can be any form of sensory feedback, e.g., visualfeedback, auditory feedback, or tactile feedback; and input from theuser can be received in any form, including acoustic, speech, or tactileinput.

Embodiments of the subject matter described in this specification can beimplemented in a computing system that includes a back end component,e.g., as a data server, or that includes a middleware component, e.g.,an application server, or that includes a front end component, e.g., aclient computer having a graphical user interface or a Web browserthrough which a user can interact with an implementation of the subjectmatter described in this specification, or any combination of one ormore such back end, middleware, or front end components. The componentsof the system can be interconnected by any form or medium of digitaldata communication, e.g., a communication network. Examples ofcommunication networks include a local area network (“LAN”) and a widearea network (“WAN”), e.g., the Internet.

The computing system can include clients and servers. A client andserver are generally remote from each other and typically interactthrough a communication network. The relationship of client and serverarises by virtue of computer programs running on the respectivecomputers and having a client-server relationship to each other.

Further details regarding PCA-based portfolio margining in accordancewith the disclosed embodiments are set forth below in connection withseveral examples.

FIG. 5 depicts a set of zero curves for margining a portfolio ofthree-month LIBOR positions in accordance with the disclosedembodiments. A PCA model is generated for a base curve 500 as describedherein. The base curve 500 is representative of the current value ofpositions in the portfolio based on the three-month LIBOR rates. The PCAmodel is then shocked to produce scenario curves for a set ofhypothetical scenarios. In this example, scenario curves 502, 504 areproduced when a level factor of the PCA model is varied or offset from abase or median value for the base curve 500. The scenario curve 502 mayresult from a positive offset, while the scenario curve 504 may resultfrom a negative offset. Scenario curves 506, 508 are produced when aslope factor of the PCA model is varied or offset.

FIG. 6 depicts a simplified representation of a distribution of returns(e.g., log returns) that has been decomposed into PCA components orfactors of a PCA model. The distribution is simplified in the sense thatonly two tenors, tenor 1 and tenor 2, are shown to allow thedistribution to be presented as a two-dimensional plot. In reality, thedimensionality of the original space presented by all the tenors is muchhigher (e.g., 23 tenors).

The PCA model is also simplified, in the sense that only two factors areshown. A first factor has an axis 600 and a second factor has an axis602. In a non-simplified example, the PCA model has one or moreadditional factors, but nonetheless reduces the dimensionality of theoriginal tenor space significantly (e.g., from 23 to 3). The first andsecond factors may correspond with the level and slope factors of thePCA model.

The PCA model is configured such that the distribution of data points inthe tenor space can be represented in the factor space. In this example,a number of data points are shown for different offsets from a basepoint (depicted as the origin). Each data point is disposed along one ofthe axes 600, 602. Each offset is one of a pair of offsets that may beused to produce a pair of scenario curves for the margin requirementdetermination. For example, offsets 604, 606 may be used to produce thecurves 502, 504 of FIG. 5. Because the offsets 604, 606 vary the firstfactor along the axis 600 independently of the second factor, eachscenario curve is factor-specific as described above. Offsets locatedfarther out on the axes 600, 602 are representative of larger shocks.Selection of the offsets 604, 606 is deemed to be sufficientlyrepresentative of the entire distribution for purposes of margincoverage.

FIG. 7 depicts respective plots of the weights or sensitivities of thethree most significant factors of a PCA model generated in accordancewith one embodiment. A first plot 700 shows the weights of the levelfactor. A second plot 702 shows the weights of the slope factor. A thirdplot 704 shows the weights of the curvature factor.

FIG. 8 depicts a charge function that may be used to support theoptimization (or reduction) of factors in the PCA models relied upon bythe disclosed embodiments. In this embodiment, the charge function is anexponential function of the tenor or maturity of a position within theportfolio. The charge function may be scaled as described above tocalculate a reserve charge used to adjust the margin requirementdetermined based on a factor-deficient PCA model.

FIGS. 9A-9C depict three back tests of one embodiment in connection withthree exemplary portfolios. FIG. 9A shows the historical profits andlosses (“PnL”) of a butterfly portfolio. FIG. 9B shows the historicalPnL of an outright portfolio. FIG. 9C shows the historical PnL of aspread portfolio. In each case, the PCA-based margin requirement isshown to cover the losses that would have been incurred by theportfolio.

The illustrations of the embodiments described herein are intended toprovide a general understanding of the structure of the variousembodiments. The illustrations are not intended to serve as a completedescription of all of the elements and features of apparatus and systemsthat utilize the structures or methods described herein. Many otherembodiments may be apparent to those of skill in the art upon reviewingthe disclosure. Other embodiments may be utilized and derived from thedisclosure, such that structural and logical substitutions and changesmay be made without departing from the scope of the disclosure.Additionally, the illustrations are merely representational and may notbe drawn to scale. Certain proportions within the illustrations may beexaggerated, while other proportions may be minimized. Accordingly, thedisclosure and the figures are to be regarded as illustrative ratherthan restrictive.

While this specification contains many specifics, these should not beconstrued as limitations on the scope of the invention or of what may beclaimed, but rather as descriptions of features specific to particularembodiments of the invention. Certain features that are described inthis specification in the context of separate embodiments can also beimplemented in combination in a single embodiment. Conversely, variousfeatures that are described in the context of a single embodiment canalso be implemented in multiple embodiments separately or in anysuitable sub-combination. Moreover, although features may be describedabove as acting in certain combinations and even initially claimed assuch, one or more features from a claimed combination can in some casesbe excised from the combination, and the claimed combination may bedirected to a sub-combination or variation of a sub-combination.

Similarly, while operations are depicted in the drawings and describedherein in a particular order, this should not be understood as requiringthat such operations be performed in the particular order shown or insequential order, or that all illustrated operations be performed, toachieve desirable results. In certain circumstances, multitasking andparallel processing may be advantageous. Moreover, the separation ofvarious system components in the embodiments described above should notbe understood as requiring such separation in all embodiments, and itshould be understood that the described program components and systemscan generally be integrated together in a single software product orpackaged into multiple software products.

One or more embodiments of the disclosure may be referred to herein,individually and/or collectively, by the term “invention” merely forconvenience and without intending to voluntarily limit the scope of thisapplication to any particular invention or inventive concept. Moreover,although specific embodiments have been illustrated and describedherein, it should be appreciated that any subsequent arrangementdesigned to achieve the same or similar purpose may be substituted forthe specific embodiments shown. This disclosure is intended to cover anyand all subsequent adaptations or variations of various embodiments.Combinations of the above embodiments, and other embodiments notspecifically described herein, will be apparent to those of skill in theart upon reviewing the description.

The Abstract of the Disclosure is provided to comply with 37 C.F.R. §1.72(b) and is submitted with the understanding that it will not be usedto interpret or limit the scope or meaning of the claims. In addition,in the foregoing Detailed Description, various features may be groupedtogether or described in a single embodiment for the purpose ofstreamlining the disclosure. This disclosure is not to be interpreted asreflecting an intention that the claimed embodiments require morefeatures than are expressly recited in each claim. Rather, as thefollowing claims reflect, inventive subject matter may be directed toless than all of the features of any of the disclosed embodiments. Thus,the following claims are incorporated into the Detailed Description,with each claim standing on its own as defining separately claimedsubject matter.

It is therefore intended that the foregoing detailed description beregarded as illustrative rather than limiting, and that it be understoodthat it is the following claims, including all equivalents, that areintended to define the spirit and scope of this invention.

What is claimed is:
 1. A computer implemented method for determining amargin requirement for a financial product portfolio, wherein marketconditions for the financial product portfolio are characterized by azero curve, the computer implemented method comprising: producing, witha processor, a plurality of scenario curves, each scenario curve beingproduced from a principal component analysis (PCA) model of the zerocurve by varying a respective PCA factor of a plurality of PCA factorsof the PCA model; calculating a respective projected value of thefinancial product portfolio for each scenario curve of the plurality ofscenario curves; calculating, for each PCA factor, a loss risk amountbased on a current value of the financial product portfolio and theprojected values calculated for those scenario curves of the pluralityof scenario curves produced by varying the PCA factor for which the lossrisk amount is being calculated; and determining the margin requirementbased on a sum of the loss risk amounts for the plurality of PCAfactors.
 2. The computer implemented method of claim 1 wherein producingthe plurality of scenario curves comprises producing, for each PCAfactor, a first scenario curve by varying the PCA factor by a positiveoffset and a second scenario curve by varying the PCA factor by anegative offset. The computer implemented method of claim 1 whereinproducing the plurality of scenario curves comprises obtaining an offsetfor each PCA factor to produce each scenario curve.
 4. The computerimplemented method of claim 3 wherein the offset for each PCA factorfalls in a range from about two to about four standard deviations of adistribution of the PCA factor.
 5. The computer implemented method ofclaim 1 wherein, with respect to each scenario curve, each PCA factor ofthe plurality of PCA factors other than the varied PCA factor is notvaried.
 6. The computer implemented method of claim 1 wherein theplurality of scenario curves comprises a pair of scenario curves foreach PCA factor. The computer implemented method of claim 6 wherein therespective PCA factor is varied by an equal and opposite offset in eachscenario curve of the pair of scenario curves.
 8. The computerimplemented method of claim 6 wherein calculating the loss risk amountfor each PCA factor comprises: determining gain and loss amounts foreach PCA factor based on the pair of scenario curves; and taking theabsolute value of the loss amount.
 9. The computer implemented method ofclaim 1 further comprising generating the PCA model based on decayedhistorical return data.
 10. The computer implemented method of claim 1wherein the PCA model is configured as a factor-deficient model.
 11. Thecomputer implemented method of claim 1 wherein the PCA model does notinclude PCA factors beyond level, slope, and curvature.
 12. The computerimplemented method of claim 1 wherein determining the margin requirementcomprises: calculating a reserve charge for a tenor in the financialproduct portfolio; and adding the reserve charge to the sum of the lossrisk amounts.
 13. A system for determining a margin requirement forfinancial product portfolio, wherein market conditions for the financialproduct portfolio are characterized by a zero curve, the systemcomprising a processor and a memory coupled with the processor, thesystem further comprising: first logic stored in the memory andexecutable by the processor to generate a principal component analysis(PCA) model of the zero curve, the PCA model comprising a plurality ofPCA factors; second logic stored in the memory and executable by theprocessor to produce a plurality of scenario curves, each scenario curvebeing produced from the PCA model by varying a respective one of theplurality of PCA factors; third logic stored in the memory andexecutable by the processor to calculate a respective projected value ofthe financial product portfolio for each scenario curve of the pluralityof scenario curves; fourth logic stored in the memory and executable bythe processor to calculate, for each PCA factor, a loss risk amountbased on a current value of the financial product portfolio and theprojected values calculated for those scenario curves of the pluralityof scenario curves producing by varying the PCA factor for which theloss risk amount is being calculated; and fifth logic stored in thememory and executable by the processor to determine the marginrequirement based on a sum of the loss risk amounts for the plurality ofPCA factors.
 14. The system of claim 13 wherein the second logic isfurther executable by the processor to produce, for each PCA factor, afirst scenario curve by varying the PCA factor by a positive offset anda second scenario curve by varying the PCA factor by a negative offset.15. The system of claim 13 wherein the second logic is furtherexecutable by the processor to obtain an offset for each PCA factor toproduce each scenario curve.
 16. The system of claim 15 wherein theoffset for each PCA factor falls in a range from about two to about fourstandard deviations of a distribution of the PCA factor.
 17. The systemof claim 13 wherein, with respect to each scenario curve, each PCAfactor of the plurality of PCA factors other than the varied PCA factoris not varied.
 18. The system of claim 13 wherein: the plurality ofscenario curves comprises a pair of scenario curves for each PCA factor;and the respective PCA factor is varied by an equal and opposite offsetin each scenario curve of the pair of scenario curves.
 19. The system ofclaim 13 wherein the fourth logic is further executable by the processorto determine gain and loss amounts for each PCA factor based on the pairof scenario curves, and take the absolute value of the loss amount. 20.The system of claim 13 wherein the PCA model does not include PCAfactors beyond level, slope, and curvature.
 21. The system of claim 13further comprising sixth logic stored in the memory and executable bythe processor to calculate a reserve charge for a tenor in the financialproduct portfolio , and add the reserve charge to the sum of the lossrisk amounts.
 22. A system for determining a margin requirement for afinancial product portfolio, wherein market conditions for the financialproduct portfolio are characterized by a zero curve, the systemcomprising: means for producing a plurality of scenario curves, eachscenario curve being produced from a principal component analysis (PCA)model of the zero curve by varying a respective PCA factor of aplurality of PCA factors of the PCA model; means for calculating arespective projected value of the financial product portfolio for eachscenario curve of the plurality of scenario curves; means forcalculating, for each PCA factor, a loss risk amount based on a currentvalue of the financial product portfolio and the projected valuescalculated for those scenario curves of the plurality of scenario curvesproducing by varying the PCA factor for which the loss risk amount isbeing calculated; and means for determining the margin requirement basedon a sum of the loss risk amounts for the plurality of PCA factors.